Acquiring Channel State Information (CSI) in wireless communications is costly. It generally requires training that takes resources away from data transmission. Training has become an even bigger concern since the emergence of communications involving arrays with a very large number of antenna elements, for which CSI acquisition is a major research focus. In a massive MIMO (multiple inputs-multiple outputs) system, a base station equipped with a massive array communicates with a small number of users. Downlink channel training uses a training length that is proportional to the number of antennas in the massive arrays and becomes impractical.
Existing approaches use a simple iterative algorithm to extract a maximal beamforming gain achievable by two communicating arrays in a reciprocal channel, without knowledge of the channel. Starting with an arbitrary weight factor at one of the arrays transmitting to the other array, a new weight factor is created by a conjugation and normalization. The process is then repeated until convergence. The beamforming weights converge to the maximal (left and right) eigenvectors of the channel matrix. It is just like a ping pong game between two devices, where, at each iteration, a device simply returns the conjugate of the signals that it just received. The beauty of this approach resides in the extreme simplicity it takes to estimate the maximal eigenvectors of the channel matrix.
In existing approaches, a bilateral training procedure is used to directly estimate the beamforming vectors by optimizing the maximum signal-to-interference-plus-noise ratio (SINR) algorithm for the MIMO interference channel. Although it is an efficient procedure for a small number of antennas, it becomes computationally heavy when massive arrays are involved.